The real number \(k\) for which the equation, \(2x^{3}+3x+k=0\) has two distinct real roots in \([0,1]\)

1
lies between \(2\) and \(3\)
2
lies between \(1\) and \(0\)
3
does not exist
4
lies between \(1\) and \(2\)

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